Eaton's Method

Part 4, Part 4: Pore Pressure

Learning objectives

Fit a normal compaction trend to the sonic or resistivity of clean shale
Apply Eaton's equation: pore pressure is the overburden minus the effective stress the velocity implies
Use the sonic exponent of 3 and read the canon teaching case: velocity ratio 0.9 gives 40.4 MPa
State Eaton's built-in assumption, undercompaction, and where it breaks

Velocity In, Pressure Out

The last two sections built the physics; Eaton's method, from 1975, turns it into a number that has drilled thousands of wells. The recipe is simple. First, fit a normal compaction trend to the log of a clean shale: how fast the sonic velocity should climb, or resistivity increase, if the shale were compacting normally. Then, wherever the measured velocity falls below that trend, read the shortfall as reduced effective stress and convert it to pore pressure: $P_p = S_v - (S_v - P_{hyd})\left(\dfrac{\Delta t_n}{\Delta t}\right)^{3}$ p=Sv−(Sv−Phyd)left(dfracDeltatnDeltatright)3, or equivalently with the velocity ratio, $P_p = S_v - (S_v - P_{hyd})\left(\dfrac{v}{v_n}\right)^{3}$ p=Sv−(Sv−Phyd)left(dfracvvnright)3. The exponent 3 is Eaton's calibration for sonic data (resistivity uses 1.2), and the whole formula is one honest idea: the gap between measured velocity and the normal trend is the overpressure.

Drag the observed velocity in the figure. When it sits on the normal trend, the ratio is 1, the correction term is the full effective stress, and Eaton returns hydrostatic pressure exactly, the identity that makes the method trustworthy: no anomaly, no overpressure. Pull the velocity below trend and the pore pressure climbs. The canon teaching case: a velocity ratio of 0.9 at our 3 km depth, with the exponent 3, gives $P_p = 67.7 - 37.4\times0.729 = 40.4$ p=67.7−37.4times0.729=40.4 MPa, roughly 10 MPa of overpressure from a 10 percent velocity shortfall. The cube is unforgiving in a useful way, small velocity anomalies map to large pressure changes, which is why an accurate normal trend matters more than almost anything else in the workflow.

The Assumption, and Its Limit

Eaton's method is built on one assumption stated plainly: the overpressure was made by undercompaction, so that low velocity faithfully means high retained porosity means low effective stress. Within that world it is superb, and its transparency, one trend, one exponent, one power law, is why it remains the field default fifty years on. But recall the branch from section 4.2: if the overpressure came from unloading, gas generation or fluid expansion, then the rock's velocity was lowered by a mechanism that does not follow the loading trend, and Eaton, reading that low velocity as undercompaction, will under-predict the pressure, sometimes dangerously. The tell is a velocity reversal, velocity actually decreasing with depth, which loading alone cannot produce. When you see it, Eaton is the wrong tool and Bowers, next section, is the right one. Choosing between them by reading the velocity trend's shape is the professional skill this pair of sections builds.

References

Eaton, B. A. (1975). The equation for geopressure prediction from well logs. SPE 5544.
Zoback, M. D. (2007). Reservoir Geomechanics. Cambridge University Press.
Bowers, G. L. (1995). Pore pressure estimation from velocity data. SPE Drilling & Completion, 10(2), 89-95.